Quantum Matter Lecture 13

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and welcome back this is I think now the 13th lecture lecture series we were discussing hartree fock when we left off and we going to begin by applying hartree fock to a standard example which is very useful and general example which is the translationally invariant interacting Fermi gas so what we imagining in our head is describing for example electrons in a metal but we throwing out the details of the underlying the underlying crystal lattice so we don have any any ions breaking the perfect translational invariance in thinking that these are not going to be very important for the the physics we going to be interested in so it just the electrons in the system now this actually has has a little bit of a problem due to the basically due to the fact that the Coulomb interaction is a long range and the problem is as follows if you if you take start with a vacuum nothing in it just vacuum and you start adding lots of electrons we not going to put in any positive ions we just putting in lots of electrons well the problem is that the energy of this it is